Movement data analysis in R; Flights and temporal subsampling - r

Question

I want to analyse angles in movement of animals. I have tracking data that has 10 recordings per second. The data per recording consists of the position (x,y) of the animal, the angle and distance relative to the previous recording and furthermore includes speed and acceleration.
I want to analyse the speed an animal has while making a particular angle, however since the temporal resolution of my data is so high, each turn consists of a number of minute angles.
I figured there are two possible ways to work around this problem for both of which I do not know how to achieve such a thing in R and help would be greatly appreciated.
The first: Reducing my temporal resolution by a certain factor. However, this brings the disadvantage of losing possibly important parts of the data. Despite this, how would I be able to automatically subsample for example every 3rd or 10th recording of my data set?
The second: By converting straight movement into so called 'flights'; rule based aggregation of steps in approximately the same direction, separated by acute turns (see the figure). A flight between two points ends when the perpendicular distance from the main direction of that flight is larger than x, a value that can be arbitrarily set. Does anyone have any idea how to do that with the xy coordinate positional data that I have?

Answer 1

It sounds like there are three potential things you might want help with: the algorithm, the math, or R syntax.
The algorithm you need may depend on the specifics of your data. For example, how much data do you have? What format is it in? Is it in 2D or 3D? One possibility is to iterate through your data set. With each new point, you need to check all the previous points to see if they fall within your desired column. If the data set is large, however, this might be really slow. Worst case scenario, all the data points are in a single flight segment, meaning you would check the first point the same number of times as you have data points, the second point one less, etc. The means n + (n-1) + (n-2) + ... + 1 = n(n-1)/2 operations. That's O(n^2); the operating time could have quadratic growth with respect to the size of your data set. Hence, you may need something more sophisticated.
The math to check whether a point is within your desired column of x is pretty straightforward, although maybe more sophisticated math could help inform a better algorithm. One approach would be to use vector arithmetic. To take an example, suppose you have points A, B, and C. Your goal is to see if B falls in a column of width x around the vector from A to C. To do this, find the vector v orthogonal to C, then look at whether the magnitude of the scalar projection of the vector from A to B onto v is less than x. There is lots of literature available for help with this sort of thing, here is one example.
I think this is where I might start (with a boolean function for an individual point), since it seems like an R function to determine this would be convenient. Then another function that takes a set of points and calculates the vector v and calls the first function for each point in the set. Then run some data and see how long it takes.
I'm afraid I won't be of much help with R syntax, although it is on my list of things I'd like to learn. I checked out the manual for R last night and it had plenty of useful examples. I believe this is very doable, even for an R novice like myself. It might be kind of slow if you have a big data set. However, with something that works, it might also be easier to acquire help from people with more knowledge and experience to optimize it.
Two quick clarifying points in case they are helpful:
The above suggestion is just to start with the data for a single animal, so when I talk about growth of data I'm talking about the average data sample size for a single animal. If that is slow, you'll probably need to fix that first. Then you'll need to potentially analyze/optimize an algorithm for processing multiple animals afterwards.
I'm implicitly assuming that the definition of flight segment is the largest subset of contiguous data points where no "sub" flight segment violates the column rule. That is to say, I think I could come up with an example where a set of points satisfies your rule of falling within a column of width x around the vector to the last point, but if you looked at the column of width x around the vector to the second to last point, one point wouldn't meet the criteria anymore. Depending on how you define the flight segment then (e.g. if you want it to be the largest possible set of points that meet your condition and don't care about what happens inside), you may need something different (e.g. work backwards instead of forwards).